Articles | Volume 8, issue 10
https://doi.org/10.5194/wes-8-1613-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-8-1613-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
27 Oct 2023
Research article |
| 27 Oct 2023
| 27 Oct 2023
Extreme wind turbine response extrapolation with the Gaussian mixture model
Xiaodong Zhang
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Nikolay Dimitrov
CORRESPONDING AUTHOR
Department of Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark
Related authors
Xiaodong Zhang and Anand Natarajan
Wind Energ. Sci., 7, 2135–2148, https://doi.org/10.5194/wes-7-2135-2022, https://doi.org/10.5194/wes-7-2135-2022, 2022
Short summary
Short summary
Joint probability distribution of 10 min mean wind speed and the standard deviation is proposed using the Gaussian mixture model and has been shown to agree well with 15 years of measurements. The environmental contour with a 50-year return period (extreme turbulence) is estimated. The results from the model could be taken as inputs for structural reliability analysis and uncertainty quantification of wind turbine design loads.
Moritz Gräfe, Vasilis Pettas, Nikolay Dimitrov, and Po Wen Cheng
Wind Energ. Sci., 9, 2175–2193, https://doi.org/10.5194/wes-9-2175-2024, https://doi.org/10.5194/wes-9-2175-2024, 2024
Short summary
Short summary
This study explores a methodology using floater motion and nacelle-based lidar wind speed measurements to estimate the tension and damage equivalent loads (DELs) on floating offshore wind turbines' mooring lines. Results indicate that fairlead tension time series and DELs can be accurately estimated from floater motion time series. Using lidar measurements as model inputs for DEL predictions leads to similar accuracies as using displacement measurements of the floater.
Xiaodong Zhang and Anand Natarajan
Wind Energ. Sci., 7, 2135–2148, https://doi.org/10.5194/wes-7-2135-2022, https://doi.org/10.5194/wes-7-2135-2022, 2022
Short summary
Short summary
Joint probability distribution of 10 min mean wind speed and the standard deviation is proposed using the Gaussian mixture model and has been shown to agree well with 15 years of measurements. The environmental contour with a 50-year return period (extreme turbulence) is estimated. The results from the model could be taken as inputs for structural reliability analysis and uncertainty quantification of wind turbine design loads.
Davide Conti, Nikolay Dimitrov, Alfredo Peña, and Thomas Herges
Wind Energ. Sci., 6, 1117–1142, https://doi.org/10.5194/wes-6-1117-2021, https://doi.org/10.5194/wes-6-1117-2021, 2021
Short summary
Short summary
We carry out a probabilistic calibration of the Dynamic Wake Meandering (DWM) model using high-spatial- and high-temporal-resolution nacelle-based lidar measurements of the wake flow field. The experimental data were collected from the Scaled Wind Farm Technology (SWiFT) facility in Texas. The analysis includes the velocity deficit, wake-added turbulence, and wake meandering features under various inflow wind and atmospheric-stability conditions.
Davide Conti, Vasilis Pettas, Nikolay Dimitrov, and Alfredo Peña
Wind Energ. Sci., 6, 841–866, https://doi.org/10.5194/wes-6-841-2021, https://doi.org/10.5194/wes-6-841-2021, 2021
Short summary
Short summary
We define two lidar-based procedures for improving the accuracy of wind turbine load assessment under wake conditions. The first approach incorporates lidar observations directly into turbulence fields serving as inputs for aeroelastic simulations; the second approach imposes lidar-fitted wake deficit time series on the turbulence fields. The uncertainty in the lidar-based power and load predictions is quantified for a variety of scanning configurations and atmosphere turbulence conditions.
Inga Reinwardt, Levin Schilling, Dirk Steudel, Nikolay Dimitrov, Peter Dalhoff, and Michael Breuer
Wind Energ. Sci., 6, 441–460, https://doi.org/10.5194/wes-6-441-2021, https://doi.org/10.5194/wes-6-441-2021, 2021
Short summary
Short summary
This analysis validates the DWM model based on loads and power production measured at an onshore wind farm. Special focus is given to the performance of a version of the DWM model that was previously recalibrated with a lidar system at the site. The results of the recalibrated wake model agree very well with the measurements. Furthermore, lidar measurements of the wind speed deficit and the wake meandering are incorporated in the DWM model definition in order to decrease the uncertainties.
Davide Conti, Nikolay Dimitrov, and Alfredo Peña
Wind Energ. Sci., 5, 1129–1154, https://doi.org/10.5194/wes-5-1129-2020, https://doi.org/10.5194/wes-5-1129-2020, 2020
Short summary
Short summary
We propose a method for carrying out wind turbine load validation in wake conditions using measurements from forward-looking nacelle lidars. The uncertainty of aeroelastic load predictions is quantified against wind turbine on-board sensor data. This work demonstrates the applicability of nacelle-mounted lidar measurements to extend load and power validations under wake conditions and highlights the main challenges.
Laura Schröder, Nikolay Krasimirov Dimitrov, and David Robert Verelst
Wind Energ. Sci., 5, 1007–1022, https://doi.org/10.5194/wes-5-1007-2020, https://doi.org/10.5194/wes-5-1007-2020, 2020
Short summary
Short summary
We suggest a methodology for correlating loads with component reliability of turbines in wind farms by combining physical modeling with machine learning. The suggested approach is demonstrated on an offshore wind farm for comparing performance, loads and lifetime estimations against recorded main bearing failures from maintenance reports. It is found that turbines positioned at the border of the wind farm with a higher expected AEP are estimated to experience earlier main bearing failures.
Ásta Hannesdóttir, Mark Kelly, and Nikolay Dimitrov
Wind Energ. Sci., 4, 325–342, https://doi.org/10.5194/wes-4-325-2019, https://doi.org/10.5194/wes-4-325-2019, 2019
Short summary
Short summary
We investigate large wind speed fluctuations from a 10-year period at the Danish coastal site Høvsøre. The most extreme fluctuations are not turbulent but due to larger-scale weather phenomena. We find how these fluctuations impact wind turbines using simulations. The results are then compared to an extreme turbulence model described in the wind turbine safety standards, and it is found that the loads on the different turbine components are not the same as what the standard describes.
Nikolay Dimitrov, Mark C. Kelly, Andrea Vignaroli, and Jacob Berg
Wind Energ. Sci., 3, 767–790, https://doi.org/10.5194/wes-3-767-2018, https://doi.org/10.5194/wes-3-767-2018, 2018
Short summary
Short summary
Wind energy site suitability assessment procedures often require estimating the loads a wind turbine will be subject to when installed. The estimation is often time-consuming and requires several iterations. We have developed a procedure for quick and accurate estimation of site-specific wind turbine loads. Our approach employs computationally efficient parametric models that are calibrated to high-fidelity load simulations. The result is a significant reduction in computation efforts.
Alfredo Peña, Jakob Mann, and Nikolay Dimitrov
Wind Energ. Sci., 2, 133–152, https://doi.org/10.5194/wes-2-133-2017, https://doi.org/10.5194/wes-2-133-2017, 2017
Short summary
Short summary
Nacelle lidars are nowadays extensively used to scan the turbine inflow. Thus, it is important to characterize turbulence from their measurements. We present two methods to perform turbulence estimation and demonstrate them using two types of lidars. With one method we can estimate the along-wind unfiltered variance accurately. With the other we can estimate the filtered radial velocity variance accurately and velocity-tensor parameters under neutral and high wind-speed conditions.
Related subject area
Thematic area: Wind technologies | Topic: Design concepts and methods for plants, turbines, and components
One-to-one aeroservoelastic validation of operational loads and performance of a 2.8 MW wind turbine model in OpenFAST
Identification of electro-mechanical interactions in wind turbines
A sensitivity-based estimation method for investigating control co-design relevance
Validation of aeroelastic dynamic model of active trailing edge flap system tested on a 4.3 MW wind turbine
Effect of Blade Inclination Angle for Straight Bladed Vertical Axis Wind Turbines
Mesoscale modelling of North Sea wind resources with COSMO-CLM: model evaluation and impact assessment of future wind farm characteristics on cluster-scale wake losses
Gradient-based wind farm layout optimization with inclusion and exclusion zones
A novel techno-economical layout optimization tool for floating wind farm design
Hybrid-Lambda: a low-specific-rating rotor concept for offshore wind turbines
Speeding up large-wind-farm layout optimization using gradients, parallelization, and a heuristic algorithm for the initial layout
Nonlinear vibration characteristics of virtual mass systems for wind turbine blade fatigue testing
The effect of site-specific wind conditions and individual pitch control on wear of blade bearings
A neighborhood search integer programming approach for wind farm layout optimization
Enabling control co-design of the next generation of wind power plants
Offshore wind farm optimisation: a comparison of performance between regular and irregular wind turbine layouts
A data-driven reduced-order model for rotor optimization
Grand challenges in the design, manufacture, and operation of future wind turbine systems
Computational fluid dynamics (CFD) modeling of actual eroded wind turbine blades
Grand Challenges: wind energy research needs for a global energy transition
Current status and grand challenges for small wind turbine technology
CFD-based curved tip shape design for wind turbine blades
Impacts of wind field characteristics and non-steady deterministic wind events on time-varying main-bearing loads
Kenneth Brown, Pietro Bortolotti, Emmanuel Branlard, Mayank Chetan, Scott Dana, Nathaniel deVelder, Paula Doubrawa, Nicholas Hamilton, Hristo Ivanov, Jason Jonkman, Christopher Kelley, and Daniel Zalkind
Wind Energ. Sci., 9, 1791–1810, https://doi.org/10.5194/wes-9-1791-2024, https://doi.org/10.5194/wes-9-1791-2024, 2024
Short summary
Short summary
This paper presents a study of the popular wind turbine design tool OpenFAST. We compare simulation results to measurements obtained from a 2.8 MW land-based wind turbine. Measured wind conditions were used to generate turbulent flow fields through several techniques. We show that successful validation of the tool is not strongly dependent on the inflow generation technique used for mean quantities of interest. The type of inflow assimilation method has a larger effect on fatigue quantities.
Fiona Dominique Lüdecke, Martin Schmid, and Po Wen Cheng
Wind Energ. Sci., 9, 1527–1545, https://doi.org/10.5194/wes-9-1527-2024, https://doi.org/10.5194/wes-9-1527-2024, 2024
Short summary
Short summary
Large direct-drive wind turbines, with a multi-megawatt power rating, face design challenges. Moving towards a more system-oriented design approach could potentially reduce mass and costs. Exploiting the full design space, though, may invoke interaction mechanisms, which have been neglected in the past. Based on coupled simulations, this work derives a better understanding of the electro-mechanical interaction mechanisms and identifies potential for design relevance.
Jenna Iori, Carlo Luigi Bottasso, and Michael Kenneth McWilliam
Wind Energ. Sci., 9, 1289–1304, https://doi.org/10.5194/wes-9-1289-2024, https://doi.org/10.5194/wes-9-1289-2024, 2024
Short summary
Short summary
The controller of a wind turbine has an important role in regulating power production and avoiding structural failure. However, it is often designed after the rest of the turbine, and thus its potential is not fully exploited. An alternative is to design the structure and the controller simultaneously. This work develops a method to identify if a given turbine design can benefit from this new simultaneous design process. For example, a higher and cheaper turbine tower can be built this way.
Andrea Gamberini, Thanasis Barlas, Alejandro Gomez Gonzalez, and Helge Aagaard Madsen
Wind Energ. Sci., 9, 1229–1249, https://doi.org/10.5194/wes-9-1229-2024, https://doi.org/10.5194/wes-9-1229-2024, 2024
Short summary
Short summary
Movable surfaces on wind turbine (WT) blades, called active flaps, can reduce the cost of wind energy. However, they still need extensive testing. This study shows that the computer model used to design a WT with flaps aligns well with measurements obtained from a 3month test on a commercial WT featuring a prototype flap. Particularly during flap actuation, there were minimal differences between simulated and measured data. These findings assure the reliability of WT designs incorporating flaps.
Laurence Boyd Morgan, Abbas Kazemi Amiri, William Leithead, and James Carroll
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-42, https://doi.org/10.5194/wes-2024-42, 2024
Revised manuscript accepted for WES
Short summary
Short summary
This paper presents a systematic study into the effect of blade inclination angle, chord distribution, and blade length on vertical axis wind turbine performance. It is shown that for rotors of identical power production, both blade volume and rotor torque can be significantly reduced through the use of aerodynamically optimised inclined rotor blades. This demonstrates the potential of V-Rotors to reduce the cost of energy for offshore wind when compared to H-Rotors.
Ruben Borgers, Marieke Dirksen, Ine L. Wijnant, Andrew Stepek, Ad Stoffelen, Naveed Akhtar, Jérôme Neirynck, Jonas Van de Walle, Johan Meyers, and Nicole P. M. van Lipzig
Wind Energ. Sci., 9, 697–719, https://doi.org/10.5194/wes-9-697-2024, https://doi.org/10.5194/wes-9-697-2024, 2024
Short summary
Short summary
Wind farms at sea are becoming more densely clustered, which means that next to individual wind turbines interfering with each other in a single wind farm also interference between wind farms becomes important. Using a climate model, this study shows that the efficiency of wind farm clusters and the interference between the wind farms in the cluster depend strongly on the properties of the individual wind farms and are also highly sensitive to the spacing between the wind farms.
Javier Criado Risco, Rafael Valotta Rodrigues, Mikkel Friis-Møller, Julian Quick, Mads Mølgaard Pedersen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 585–600, https://doi.org/10.5194/wes-9-585-2024, https://doi.org/10.5194/wes-9-585-2024, 2024
Short summary
Short summary
Wind energy developers frequently have to face some spatial restrictions at the time of designing a new wind farm due to different reasons, such as the existence of protected natural areas around the wind farm location, fishing routes, and the presence of buildings. Wind farm design has to account for these restricted areas, but sometimes this is not straightforward to achieve. We have developed a methodology that allows for different inclusion and exclusion areas in the optimization framework.
Amalia Ida Hietanen, Thor Heine Snedker, Katherine Dykes, and Ilmas Bayati
Wind Energ. Sci., 9, 417–438, https://doi.org/10.5194/wes-9-417-2024, https://doi.org/10.5194/wes-9-417-2024, 2024
Short summary
Short summary
The layout of a floating offshore wind farm was optimized to maximize the relative net present value (NPV). By modeling power generation, losses, inter-array cables, anchors and operational costs, an increase of EUR 34.5 million in relative NPV compared to grid-based layouts was achieved. A sensitivity analysis was conducted to examine the impact of economic factors, providing valuable insights. This study contributes to enhancing the efficiency and cost-effectiveness of floating wind farms.
Daniel Ribnitzky, Frederik Berger, Vlaho Petrović, and Martin Kühn
Wind Energ. Sci., 9, 359–383, https://doi.org/10.5194/wes-9-359-2024, https://doi.org/10.5194/wes-9-359-2024, 2024
Short summary
Short summary
This paper provides an innovative blade design methodology for offshore wind turbines with very large rotors compared to their rated power, which are tailored for an increased power feed-in at low wind speeds. Rather than designing the blade for a single optimized operational point, we include the application of peak shaving in the design process and introduce a design for two tip speed ratios. We describe how enlargement of the rotor diameter can be realized to improve the value of wind power.
Rafael Valotta Rodrigues, Mads Mølgaard Pedersen, Jens Peter Schøler, Julian Quick, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 321–341, https://doi.org/10.5194/wes-9-321-2024, https://doi.org/10.5194/wes-9-321-2024, 2024
Short summary
Short summary
The use of wind energy has been growing over the last few decades, and further increase is predicted. As the wind energy industry is starting to consider larger wind farms, the existing numerical methods for analysis of small and medium wind farms need to be improved. In this article, we have explored different strategies to tackle the problem in a feasible and timely way. The final product is a set of recommendations when carrying out trade-off analysis on large wind farms.
Aiguo Zhou, Jinlei Shi, Tao Dong, Yi Ma, and Zhenhui Weng
Wind Energ. Sci., 9, 49–64, https://doi.org/10.5194/wes-9-49-2024, https://doi.org/10.5194/wes-9-49-2024, 2024
Short summary
Short summary
This paper explores the nonlinear influence of the virtual mass mechanism on the test system in blade biaxial tests. The blade theory and simulation model are established to reveal the nonlinear amplitude–frequency characteristics of the blade-virtual-mass system. Increasing the amplitude of the blade or decreasing the seesaw length will lower the resonance frequency and load of the system. The virtual mass also affects the blade biaxial trajectory.
Arne Bartschat, Karsten Behnke, and Matthias Stammler
Wind Energ. Sci., 8, 1495–1510, https://doi.org/10.5194/wes-8-1495-2023, https://doi.org/10.5194/wes-8-1495-2023, 2023
Short summary
Short summary
Blade bearings are among the most stressed and challenging components of a wind turbine. Experimental investigations using different test rigs and real-size blade bearings have been able to show that rather short time intervals of only several hours of turbine operation can cause wear damage on the raceways of blade bearings. The proposed methods can be used to assess wear-critical operation conditions and to validate control strategies as well as lubricants for the application.
Juan-Andrés Pérez-Rúa, Mathias Stolpe, and Nicolaos Antonio Cutululis
Wind Energ. Sci., 8, 1453–1473, https://doi.org/10.5194/wes-8-1453-2023, https://doi.org/10.5194/wes-8-1453-2023, 2023
Short summary
Short summary
With the challenges of ensuring secure energy supplies and meeting climate targets, wind energy is on course to become the cornerstone of decarbonized energy systems. This work proposes a new method to optimize wind farms by means of smartly placing wind turbines within a given project area, leading to more green-energy generation. This method performs satisfactorily compared to state-of-the-art approaches in terms of the resultant annual energy production and other high-level metrics.
Andrew P. J. Stanley, Christopher J. Bay, and Paul Fleming
Wind Energ. Sci., 8, 1341–1350, https://doi.org/10.5194/wes-8-1341-2023, https://doi.org/10.5194/wes-8-1341-2023, 2023
Short summary
Short summary
Better wind farms can be built by simultaneously optimizing turbine locations and control, which is currently impossible or extremely challenging because of the size of the problem. The authors present a method to determine optimal wind farm control as a function of the turbine locations, which enables turbine layout and control to be optimized together by drastically reducing the size of the problem. In an example, a wind farm's performance improves by 0.8 % when optimized with the new method.
Maaike Sickler, Bart Ummels, Michiel Zaaijer, Roland Schmehl, and Katherine Dykes
Wind Energ. Sci., 8, 1225–1233, https://doi.org/10.5194/wes-8-1225-2023, https://doi.org/10.5194/wes-8-1225-2023, 2023
Short summary
Short summary
This paper investigates the effect of wind farm layout on the performance of offshore wind farms. A regular farm layout is compared to optimised irregular layouts. The irregular layouts have higher annual energy production, and the power production is less sensitive to wind direction. However, turbine towers require thicker walls to counteract increased fatigue due to increased turbulence levels in the farm. The study shows that layout optimisation can be used to maintain high-yield performance.
Nicholas Peters, Christopher Silva, and John Ekaterinaris
Wind Energ. Sci., 8, 1201–1223, https://doi.org/10.5194/wes-8-1201-2023, https://doi.org/10.5194/wes-8-1201-2023, 2023
Short summary
Short summary
Wind turbines have increasingly been leveraged as a viable approach for obtaining renewable energy. As such, it is essential that engineers have a high-fidelity, low-cost approach to modeling rotor load distributions. In this study, such an approach is proposed. This modeling approach was shown to make high-fidelity predictions at a low computational cost for rotor distributed-pressure loads as rotor geometry varied, allowing for an optimization of the rotor to be completed.
Paul Veers, Carlo L. Bottasso, Lance Manuel, Jonathan Naughton, Lucy Pao, Joshua Paquette, Amy Robertson, Michael Robinson, Shreyas Ananthan, Thanasis Barlas, Alessandro Bianchini, Henrik Bredmose, Sergio González Horcas, Jonathan Keller, Helge Aagaard Madsen, James Manwell, Patrick Moriarty, Stephen Nolet, and Jennifer Rinker
Wind Energ. Sci., 8, 1071–1131, https://doi.org/10.5194/wes-8-1071-2023, https://doi.org/10.5194/wes-8-1071-2023, 2023
Short summary
Short summary
Critical unknowns in the design, manufacturing, and operation of future wind turbine and wind plant systems are articulated, and key research activities are recommended.
Kisorthman Vimalakanthan, Harald van der Mijle Meijer, Iana Bakhmet, and Gerard Schepers
Wind Energ. Sci., 8, 41–69, https://doi.org/10.5194/wes-8-41-2023, https://doi.org/10.5194/wes-8-41-2023, 2023
Short summary
Short summary
Leading edge erosion (LEE) is one of the most critical degradation mechanisms that occur with wind turbine blades. A detailed understanding of the LEE process and the impact on aerodynamic performance due to the damaged leading edge is required to optimize blade maintenance. Providing accurate modeling tools is therefore essential. This novel study assesses CFD approaches for modeling high-resolution scanned LE surfaces from an actual blade with LEE damages.
Paul Veers, Katherine Dykes, Sukanta Basu, Alessandro Bianchini, Andrew Clifton, Peter Green, Hannele Holttinen, Lena Kitzing, Branko Kosovic, Julie K. Lundquist, Johan Meyers, Mark O'Malley, William J. Shaw, and Bethany Straw
Wind Energ. Sci., 7, 2491–2496, https://doi.org/10.5194/wes-7-2491-2022, https://doi.org/10.5194/wes-7-2491-2022, 2022
Short summary
Short summary
Wind energy will play a central role in the transition of our energy system to a carbon-free future. However, many underlying scientific issues remain to be resolved before wind can be deployed in the locations and applications needed for such large-scale ambitions. The Grand Challenges are the gaps in the science left behind during the rapid growth of wind energy. This article explains the breadth of the unfinished business and introduces 10 articles that detail the research needs.
Alessandro Bianchini, Galih Bangga, Ian Baring-Gould, Alessandro Croce, José Ignacio Cruz, Rick Damiani, Gareth Erfort, Carlos Simao Ferreira, David Infield, Christian Navid Nayeri, George Pechlivanoglou, Mark Runacres, Gerard Schepers, Brent Summerville, David Wood, and Alice Orrell
Wind Energ. Sci., 7, 2003–2037, https://doi.org/10.5194/wes-7-2003-2022, https://doi.org/10.5194/wes-7-2003-2022, 2022
Short summary
Short summary
The paper is part of the Grand Challenges Papers for Wind Energy. It provides a status of small wind turbine technology in terms of technical maturity, diffusion, and cost. Then, five grand challenges that are thought to be key to fostering the development of the technology are proposed. To tackle these challenges, a series of unknowns and gaps are first identified and discussed. Improvement areas are highlighted, within which 10 key enabling actions are finally proposed to the wind community.
Mads H. Aa. Madsen, Frederik Zahle, Sergio González Horcas, Thanasis K. Barlas, and Niels N. Sørensen
Wind Energ. Sci., 7, 1471–1501, https://doi.org/10.5194/wes-7-1471-2022, https://doi.org/10.5194/wes-7-1471-2022, 2022
Short summary
Short summary
This work presents a shape optimization framework based on computational fluid dynamics. The design framework is used to optimize wind turbine blade tips for maximum power increase while avoiding that extra loading is incurred. The final results are shown to align well with related literature. The resulting tip shape could be mounted on already installed wind turbines as a sleeve-like solution or be conceived as part of a modular blade with tips designed for site-specific conditions.
Edward Hart, Adam Stock, George Elderfield, Robin Elliott, James Brasseur, Jonathan Keller, Yi Guo, and Wooyong Song
Wind Energ. Sci., 7, 1209–1226, https://doi.org/10.5194/wes-7-1209-2022, https://doi.org/10.5194/wes-7-1209-2022, 2022
Short summary
Short summary
We consider characteristics and drivers of loads experienced by wind turbine main bearings using simplified models of hub and main-bearing configurations. Influences of deterministic wind characteristics are investigated for 5, 7.5, and 10 MW turbine models. Load response to gusts and wind direction changes are also considered. Cubic load scaling is observed, veer is identified as an important driver of load fluctuations, and strong links between control and main-bearing load response are shown.
Cited articles
Akaike, H.: Information theory and an extension of the maximum likelihood principle, in: Selected papers of hirotugu akaike, Springer, New York, NY, 199–213, https://doi.org/10.1007/978-1-4612-1694-0_15, 1998. a
Arthur, D. and Vassilvitskii, S.: K-means++: The advantages of careful seeding, in: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics, 1027–1035, ISBN 978-0-89871-624-5, 2007. a
Barone, M. F., Paquette, J. A., Resor, B. R., and Manuel, L.: Decades of wind turbine load simulation, in: 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Aerospace Sciences Meetings, No. SAND2011-3780C, https://doi.org/10.2514/6.2012-1288, 2011. a, b, c
Cui, M., Feng, C., Wang, Z., and Zhang, J.: Statistical representation of wind power ramps using a generalized Gaussian mixture model, IEEE T. Sustain. Energ., 9, 261–272, https://doi.org/10.1109/TSTE.2017.2727321, 2018. a
Dai, B., Xia, Y., and Li, Q.: An extreme value prediction method based on clustering algorithm, Reliab. Eng. Syst. Safe, 222, 108442, https://doi.org/10.1016/j.ress.2022.108442, 2022. a
Dempster, A. P., Laird, N. M., and Rubin, D. B.: Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Stat. Soc. B Met., 39, 1–22, https://doi.org/10.1111/j.2517-6161.1977.tb01600.x, 1977. a
Dimitrov, N.: Comparative analysis of methods for modelling the short-term probability distribution of extreme wind turbine loads: Methods for modelling the probability distribution of extreme loads, Wind Energy, 19, 717–737, https://doi.org/10.1002/we.1861, 2016. a, b, c
Ding, J. and Chen, X.: Assessing small failure probability by importance splitting method and its application to wind turbine extreme response prediction, Eng. Struct., 54, 180–191, https://doi.org/10.1016/j.engstruct.2013.03.051, 2013. a
Ding, J., Gong, K., and Chen, X.: Comparison of statistical extrapolation methods for the evaluation of long-term extreme response of wind turbine, Eng. Struct., 57, 100–115, https://doi.org/10.1016/j.engstruct.2013.09.017, 2013. a
Ditlevsen, O. and Bjerager, P.: Methods of structural systems reliability, Struct. Saf., 3, 195–229, https://doi.org/10.1016/0167-4730(86)90004-4, 1986. a
Fogle, J., Agarwal, P., and Manuel, L.: Towards an improved understanding of statistical extrapolation for wind turbine extreme loads, Wind Energy, 11, 613–635, https://doi.org/10.1002/we.303, 2008. a
Freudenreich, K. and Argyriadis, K.: Wind turbine load level based on extrapolation and simplified methods, Wind Energy, 11, 589–600, https://doi.org/10.1002/we.279, 2008. a, b, c
Gupta, L. and Sortrakul, T.: A gaussian-mixture-based image segmentation algorithm, Pattern Recogn., 31, 315–325, https://doi.org/10.1016/S0031-3203(97)00045-9, 1998. a
He, X., Cai, D., Shao, Y., Bao, H., and Han, J.: Laplacian regularized Gaussian mixture model for data clustering, IEEE T. Knowl. Data En., 23, 1406–1418, https://doi.org/10.1109/TKDE.2010.259, 2011. a
Huang, Y., Englehart, K., Hudgins, B., and Chan, A.: A Gaussian mixture model based classification scheme for myoelectric control of powered upper limb prostheses, IEEE T. Bio.-Med. Eng., 52, 1801–1811, https://doi.org/10.1109/TBME.2005.856295, 2005. a
Jung, C. and Schindler, D.: Global comparison of the goodness-of-fit of wind speed distributions, Energ. Convers. Manage., 133, 216–234, https://doi.org/10.1016/j.enconman.2016.12.006, 2017. a
Kim, S. C. and Kang, T. J.: Texture classification and segmentation using wavelet packet frame and Gaussian mixture model, Pattern Recogn., 40, 1207–1221, https://doi.org/10.1016/j.patcog.2006.09.012, 2007. a
Moriarty, P. J., Holley, W. E., and Butterfield, S. P.: Extrapolation of extreme and fatigue loads using probabilistic methods, Technical Report, No. NREL/TP-500-34421, https://doi.org/10.2172/15011693, 2004. a
Naess, A., Gaidai, O., and Karpa, O.: Estimation of extreme values by the average conditional exceedance rate method, J. Prob. Stat., 2013, 797014, https://doi.org/10.1155/2013/797014, 2013. a
Natarajan, A. and Holley, W. E.: Statistical extreme load extrapolation with quadratic distortions for wind turbines, J. Sol. Energ.-T. ASME, 130, 0310171–0310177, https://doi.org/10.1115/1.2931513, 2008. a
Nguyen, T. M. and Wu, Q. M.: Fast and robust spatially constrained gaussian mixture model for image segmentation, IEEE T. Circ. Syst. Vid., 23, 621–635, https://doi.org/10.1109/TCSVT.2012.2211176, 2013. a
Permuter, H., Francos, J., and Jermyn, I.: A study of Gaussian mixture models of color and texture features for image classification and segmentation, Pattern Recogn., 39, 695–706, https://doi.org/10.1016/j.patcog.2005.10.028, 2006. a
Srbinovski, B., Temko, A., Leahy, P., Pakrashi, V., and Popovici, E.: Gaussian mixture models for site-specific wind turbine power curves, P. I. Mech. Eng. A-J. Pow., 235, 494–505, https://doi.org/10.1177/0957650920931729, 2021. a
Toft, H. S., Sørensen, J. D., and Veldkamp, D.: Assessment of load extrapolation methods for wind turbines, J. Sol. Energ.-T. ASME, 133, 021001, https://doi.org/10.1115/1.4003416, 2011. a
van Eijk, S. F., Bos, R., and Bierbooms, W. A. A. M.: The risks of extreme load extrapolation, Wind Energ. Sci., 2, 377–386, https://doi.org/10.5194/wes-2-377-2017, 2017. a
Wackerly, D., Mendenhall, W., and Scheaffer, R. L.: Mathematical Statistics with Applications, Thomson, 912 pp., ISBN 0-495-38508-5, 2008. a
Wahbah, M., Alhussein, O., El-Fouly, T. H., Zahawi, B., and Muhaidat, S.: Evaluation of parametric statistical models for wind speed probability density estimation, 2018 IEEE Electrical Power and Energy Conference, Toronto, ON, Canada, 1–6, https://doi.org/10.1109/EPEC.2018.8598283, 2018. a
Weber, C., Ray, D., Valverde, A., Clark, J., and Sharma, K.: Gaussian mixture model clustering algorithms for the analysis of high-precision mass measurements, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Nucl. Instrum. Methods, 1027, 166299, https://doi.org/10.1016/j.nima.2021.166299, 2022. a
Yang, Q., Li, Y., Li, T., Zhou, X., Huang, G., and Lian, J.: Statistical extrapolation methods and empirical formulae for estimating extreme loads on operating wind turbine towers, Eng. Struct., 267, 114667, https://doi.org/10.1016/j.engstruct.2022.114667, 2022. a, b
Yin, S., Zhang, Y., and Karim, S.: Large scale remote sensing image segmentation based on fuzzy region competition and gaussian mixture model, IEEE Access, 6, 26069–26080, https://doi.org/10.1109/ACCESS.2018.2834960, 2018. a
Zhang, J., Yan, J., Infield, D., Liu, Y., and Sang Lien, F.: Short-term forecasting and uncertainty analysis of wind turbine power based on long short-term memory network and Gaussian Mixture Model, Appl. Energ., 241, 229–244, https://doi.org/10.1016/j.apenergy.2019.03.044, 2019. a
Zhang, X. and Natarajan, A.: Gaussian mixture model for extreme wind turbulence estimation, Wind Energ. Sci., 7, 2135–2148, https://doi.org/10.5194/wes-7-2135-2022, 2022. a
Zhang, X., Low, Y. M., and Koh, C. G.: Maximum entropy distribution with fractional moments for reliability analysis, Struct. Saf., 83, 101904, https://doi.org/10.1016/j.strusafe.2019.101904, 2020. a, b
Zhang, Y., Li, M., Wang, S., Dai, S., Luo, L., Zhu, E., Xu, H., Zhu, X., Yao, C., and Zhou, H.: Gaussian mixture model clustering with incomplete data, ACM T. Multim. Comput., 17, 1–14, 2021. a
Short summary
Wind turbine extreme response estimation based on statistical extrapolation necessitates using a small number of simulations to calculate a low exceedance probability. This is a challenging task especially if we require small prediction error. We propose the use of a Gaussian mixture model as it is capable of estimating a low exceedance probability with minor bias error, even with limited simulation data, having flexibility in modeling the distributions of varying response variables.
Wind turbine extreme response estimation based on statistical extrapolation necessitates using a...
Altmetrics
Final-revised paper
Preprint